How to create a moving reflection on a glass surface?
Use an object that is reflected on the surface.

Step 1: use a glossy material on the surface that you want to be reflective. 

Step 2: create one or more planes with the shape you need, use an emissive material for them, and place them in a way that are visible as reflections on the surface of the reflective object. 

Step 3: animate the position of the emissive plane so that it does what you need.





Read these related posts: 

https://blender.stackexchange.com/a/91173/1853

and

Why does an object with a glossy shader render in black?